Subspace estimation is coming to play an important role in a variety of modern signal processing applications. Various algorithms are proposed for efficiently tracking the principal singular values and the associated left (or right) singular vectors of successive data matrices formed from observations of a nonstationary signal in nonstationary noise. The ability to perform this tracking in real-time and with sufficient accuracy is required for many signal processing applications in technology areas such as communications, radar, sonar, and speech processing.
In some of these applications, the component of the data referred to as the “signal” may actually be nonstationary interference. The subspace of that interference signal may be tracked for the purpose of suppressing that particular interference, rather than enhancing the signal or estimating its parameters. An important attribute of these tracking algorithms is the ability to track the possibly changing dimension of the signal subspace.
Many subspace tracking algorithms are proposed in the literature, but each are associated with one or more problems. For example, the projection approximation subspace tracker (PAST) algorithm and its variant PASTd can be used for subspace tracking, and employ only basic arithmetic computations. However, PAST algorithms may not provide the desired level of accuracy. A rank-adaptive fast subspace tracking (FST) algorithm is also available. However, the FST algorithm does not estimate eigenvalues or singular values.
The fast approximate subspace tracking (FAST) algorithm and its variant FAST2 can be used for tracking singular values, singular vectors, and the dimension of a signal subspace through an overlapping sequence of data matrices. The speed and accuracy of the FAST algorithm appear to be superior or at least comparable to other algorithms such as the PAST and PASTd algorithms, FST algorithm, and the Prony-Lanczos (PL) algorithm. However, it is unclear how to implement an architecture that can address the unique computational elements of the FAST algorithm. Exacerbating this problem is that each of the computational elements should scale with the rank and size of the subspace.
Simply stated, there are no currently available solutions for real-time implementations of a subspace tracker. What is needed, therefore, is a real-time implementation of a subspace tracker.